# Transitivity

Transitivity may refer to:

## In logic and mathematics

• Transitive relation. A binary relation is transitive if whenever A is related to B and B is related to C, then A is related to C, for all A, B, and C in the domain of the relation.
• Arc-transitive graph
• Edge-transitive graph
• Ergodic theory, a group action that is metrically transitive
• Vertex-transitive graph
• A group G acts transitively on a set S if for any x, yS, there is some gG such that gx = y. See group action. A somewhat related meaning is explained at ergodic theory.
• A transitive set is a set A such that whenever xA, and yx, then yA. The smallest transitive set containing a set A is called the transitive closure of A.
• A discrete dynamical system f is topologically transitive if every open subset U' of the phase space intersects every other open subset V, when going along trajectory, i.e. there exists an integer n, for which $f^n(U)\cap V\neq\emptyset$.

## Other

• Transitive Corporation, a computer software firm that developed QuickTransit